|Fig. A: Results from G4LECS compared to G4LowEnergy.|
|Fig. B: Results from G4LECS compared to G4Penelope.|
This page describes results from a few tests that were performed to validate the G4LECS simulation code. The test program is based on the example program "Compt" included in the G4LECS package.
The simulation geometry is meant to approximate the experimental setup of Namito et al.(1994, 1995). In this experiment, a monochromatic photons beam is scattered from a target disk, and then measured with two small germanium detectors. The detectors are arranged, along with lead collimators, such that only photons that are deflected almost exactly 90 deg from the target are detected. The target disk is oriented such that each detector normal vector intersects the same target thickness. Various target materials were employed with the goal of measuring the incoherent (i.e., Compton) scattering function versus energy.
|Fig. 1: Simulation geometry from GEANT4 visualization.|
In the G4LECS simulation, the true experimental setup is approximated by a conical shell target (same thickness as the experiment) surrounded by an annular ring of germanium detector and lead collimator (Figure 1). The angle of the conical shell target is 45 deg, similar to the orientation of the disk target in the experiment. A circular photon beam in the simulation is incident on the angled sides of the conical target so as to approximate the beam/target configuration of the experiment. In this approximation, the detection efficiency is much greater than in the real experiment, but the geometry is similar. Some small differences, particularly for multiply scattered photons are to be expected.
|Fig. 2: Results for carbon target.|
Three test cases were performed with 40 keV incident photons and targets made of: carbon (0.589 mm thick), copper (2.0 mm thick), and lead (0.5 mm thick). In each case, incident photons were generated until 10,000 events were registered that deposited energy in both the target and the germanium detector. The simulations were performed for two cases: with G4LECS for the Compton and Rayleigh processes, and with the G4LowEnergy versions included with GEANT4.4.1. In each case, the remaining electromagnetic processes (i.e., photoelectric, ionization, multiple scattering, etc.) were the G4LowEnergy versions from GEANT4.1.1. The simulation results for the energy deposited in the germanium detector are compared with experimental data in Figures 2-4. In the figures, the simulated germanium energy deposits have been broadend by a Gaussian smearing function that corresponds to the resolution of the germanium detectors (0.35 keV FWHM).
|Fig. 3: Results for copper target.|
In each of the figures the peak at 40 keV corresponds to Rayleigh-scattered photons that loose no energy in the interaction, and thus deposit their full energy in the germanium. The peak near 37 keV corresponds to the most likely energy of a 90 deg Compton scattered photon (i.e., zero bound electron momentum). In the case of copper and lead, there are additional x-ray escape features near 30 keV. In the case of carbon, there is a feature near 32 keV due to multiply scattered photons.
As can be seen in the figures, there is good agreement between the data and the G4LECS simulation. The small differences that do exist are probably due to statistical fluctuations, or differences between the simulation and experimental geometries. Comparison between the G4LECS and G4LowEnergy results dramatically illustrate the effects of Dopper broadening, which causes a significant spread in the Compton-scattered photon energies that increases with the Z of the target material. The approximate FWHM of the scattered photon energy distributions are 1.2 keV, 1.5 keV, and 1.8 keV for C, Cu, and Pb, respectively.
|Fig. 4: Results for lead target.|
Once initiated by reading and collecting the required datasets, the additional computational burden in simulating Compton scattering with Doppler broading is small. For the three test cases discussed above, the G4LECS runs required an average of 5.3 percent more CPU time than the same runs using G4LowEnergyCompton. This should be an acceptable burden for all practical applications.
Longo, F., Pandola, L., and Grazia Pia, M., "New Geant4 Developments for Doppler Broadening Simulation in Compton Scattering -- Development of Charge Transfer Simulation Models in Geant4," IEEE Nucl. Sci. Symp. Conf. Record N41-2 (2009).
Namito, Y., Ban, S., and Hirayama, H., et al., "Compton Scattering of 20- to 40-keV Photons," Phys. Rev. A 51, 4, p. 3036 (1995).
Namito, Y., Ban, S., and Hirayama, H., "Implementation of the Doppler Broadening of a Compton-scattered Photon into the EGS4 Code," Nucl. Inst. Meth. A 349, p. 489 (1994).
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Author: R. Marc Kippen
Last modified: 23-Dec-2009